Resistance dimensions of branching processes in varying environments trees

Abstract

In this paper we pursue our study, in Konsowa and Oraby 2003a. [Dimensions of random trees. Statist. Probab. Lett. 62(1), 49–60] and Konsowa and Oraby 2003b. [Fractal dimensions and random walks on random trees. J. Statist. Plann. Inference 116(2), 333–342], on dimensions of some random trees. These dimensions are, for polynomially growing graphs, closely related to the type (transience-recurrence) problem of the simple random walk on such graphs. We give an interval estimation for the mean resistance dimension of branching processes in varying environments trees.